Dear Gap Forum, dear Edgar,
I am interested in finding the irreducible representations of GL(2,n) -
the group of 2-by-2 invertible matrices with integer entries modulo n.
Here, n is not necessarily a power of a prime number. How can I use Gap
to find these irreducible representations?
As far as I know, up to now there is no built-in automatic mechanism
in GAP to compute the irreducible representations of an arbitrary
finite group. (The situation is different for special classes of
groups, which unfortunately the GL_2(Z/nZ)'s do not belong to.) But
there are so-called `MeatAxe' techniques available to find irreducible
representations rather comfortably by hand. There is a GAP share
package which works over finite fields, and I have (private, still)
programs which (are supposed to) do the job over the rationals and
finite extension fields thereof.
These programs might be useful for the examples you have, Edgar; if
you are interested, please do not hesitate to contact me. Possibly I
can then give you more specific advice.
Best, J"urgen M"uller.